Question

Cost of debt using both methods​ (YTM and the approximation​ formula)   ​Currently, Warren Industries can sell 15 year​, ​$1000​-par-value bonds paying annual interest at a 8​% coupon rate. Because current market rates for similar bonds are just under 8​%, Warren can sell its bonds for ​$1030 ​each; Warren will incur flotation costs of ​$20 per bond. The firm is in the 29​% tax bracket.

a.  Find the net proceeds from the sale of the​ bond, Upper Nd.

b.  Calculate the​ bond's yield to maturity​ (YTM​) to estimate the​ before-tax and​ after-tax costs of debt.

c.  Use the approximation formula to estimate the​ before-tax and​ after-tax costs of debt.

Answer 1

Answer a.

Net Proceeds = Current Price - Flotation Costs
Net Proceeds = $1,030 - $20
Net Proceeds = $1,010

Answer b.

Face Value = $1,000
Net Proceeds = $1,010

Annual Coupon Rate = 8%
Annual Coupon = 8% * $1,000
Annual Coupon = $80

Time to Maturity = 15 years

Let Annual YTM be i%

$1,010 = $80 * PVIFA(i%, 15) + $1,000 * PVIF(i%, 15)

Using financial calculator:
N = 15
PV = -1010
PMT = 80
FV = 1000

I = 7.88%

Annual YTM = 7.88%

Before-tax Cost of Debt = 7.88%

After-tax Cost of Debt = 7.88% * (1 - 0.29)
After-tax Cost of Debt = 5.59%

Answer b.

Face Value, F = $1,000
Net Proceeds, P = $1,010
Annual Coupon, C = $80
Time to Maturity, n = 15 years

Approximate YTM = [C + (F - P) / n] / [(F + P) / 2]
Approximate YTM = [$80 + ($1,000 - $1,010) / 15] / [($1,000 + $1,010) / 2]
Approximate YTM = $79.333 / $1,005
Approximate YTM = 0.0789 or 7.89%

Annual YTM = 7.89%

Before-tax Cost of Debt = 7.89%

After-tax Cost of Debt = 7.89% * (1 - 0.29)
After-tax Cost of Debt = 5.60%